A Simple Gear System

Question:

Gears are important components inmany mechanical devices, from mechanical clocks to bicycles. Infact, they are present whenever a motor produces rotationalmotion.An example of a simple gear systemis shown in the figure.The bigger wheel (wheel 1) hasradius , while the smaller one (wheel 2) has radius . The two wheels have small teeth and are connectedthrough a metal chain so that when wheel 1rotates, the chain moveswith it and causes wheel 2 to rotate as well.
1.)Let wheel 1 rotate at a constant angularspeed . Find the ratio of the angular speed of wheel 1 to theangularspeed of wheel 2.Express your answer in terms of anyor all of the variables and . = ?2.) The rotation of wheel 1 is caused by atorque . Find the ratio of the torque acting on wheel 1 to thetorqueacting on wheel 2.Express your answer in terms of anyor all of the variables and .= ?3.)If the power needed to rotate wheel 1 is, whatis the ratio of the power of wheel 1 to the power of wheel2?Express your answer in terms of anyor all of the variables and .= ?

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